Phrase guide

convex envelope

noun · 2 senses · updated from the 2026-07-25 local source snapshot

Definitions and examples are grouped by meaning. Pronunciation, history, word forms, translations, descendants, synonyms, antonyms, derived terms, and related words appear whenever the source provides them.

Sound

Pronunciation

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1

noun

Meaning 1

Convex hull.

Definition source: English Wiktionary via Wiktextract

Topics: mathematical-analysis, mathematics, sciences

Examples

  • 1965 [Holt Rinehart & Winston], Robert E. Edwards, Functional Analysis: Theory and Applications, Dover, 1995, Unabridged Corrected Edition, page 561, In E the closed convex envelope of a compact (resp. weakly compact) set is τ(E,E')-complete.
  • 1987, H. G. Eggleston, S. Madan (translators), Nicolas Bourbaki, Topological Vector Spaces: Chapters 1–5, [1981, N. Bourbaki, Espaces Vectoriels Topologiques], Springer, page IR-10, Corollary 1. — The convex envelope of a subset A of E is identical with the set of linear combinations ∑iλix_i, where (x_i) is any finite family of points in A, the numbers λi>0 for all i and ∑iλi=1.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

2

noun

Meaning 2

For a given set S⊆Rn and real-valued function f defined on the convex hull conv(S), the highest-valued convex function that underestimates or equals f over S.

Definition source: English Wiktionary via Wiktextract

Qualifier: optimisation theory

Topics: mathematics, sciences

No example sentence was provided for this meaning.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

History

Etymology

No etymology was provided for this word.